

A073340


Fibonacci prime pairs: the indices of each pair differ by two and the relevant Fibonacci numbers are both prime.


3




OFFSET

1,1


COMMENTS

There are no other Fibonacci prime pairs up to Fibonacci[104911]. (See A001605.) Are there any larger terms?


REFERENCES

David Wells, The Penguin Dictionary of Curious and Interesting Numbers, p. 46 (Rev. ed. 1997)


LINKS

Table of n, a(n) for n=1..10.


EXAMPLE

The 431st Fibonacci number and the 433rd Fibonacci number are both prime and their indices differ by 2.


MATHEMATICA

Flatten[Select[Partition[Select[Range[3000], PrimeQ[Fibonacci[ # ]]&], 2, 1], #[[2]]  #[[1]] == 2 &]]


PROG

(Python)
from sympy import isprime
def afind(limit):
i, fnm2, fnm1 = 1, 1, 1
while i < limit:
if isprime(fnm2) and isprime(fnm2 + fnm1):
print(i, i+2, sep=", ", end=", ")
i, fnm2, fnm1 = i+1, fnm1, fnm2 + fnm1
afind(600) # Michael S. Branicky, Mar 05 2021


CROSSREFS

Cf. A000045, A001605, A279795, A281087.
Sequence in context: A069201 A272882 A077800 * A118409 A162779 A158284
Adjacent sequences: A073337 A073338 A073339 * A073341 A073342 A073343


KEYWORD

more,nonn


AUTHOR

Harvey P. Dale, Aug 25 2002


EXTENSIONS

Offset changed to 1 by Joerg Arndt, Jan 18 2017
a(1) and a(2) prepended by Bobby Jacobs, Jan 18 2017


STATUS

approved



